/**
 * Copyright 2017 Google Inc. All Rights Reserved.
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

/**
 * @file Pre-computed lookup tables for encoding ambisonic sources.
 * @author Andrew Allen <bitllama@google.com>
 */

'use strict';


/**
 * Pre-computed Spherical Harmonics Coefficients.
 *
 * This function generates an efficient lookup table of SH coefficients. It
 * exploits the way SHs are generated (i.e. Ylm = Nlm * Plm * Em). Since Nlm
 * & Plm coefficients only depend on theta, and Em only depends on phi, we
 * can separate the equation along these lines. Em does not depend on
 * degree, so we only need to compute (2 * l) per azimuth Em total and
 * Nlm * Plm is symmetrical across indexes, so only positive indexes are
 * computed ((l + 1) * (l + 2) / 2 - 1) per elevation.
 * @type {Float32Array}
 */
exports.SPHERICAL_HARMONICS =
[
  [
    [0.000000, 0.000000, 0.000000, 1.000000, 1.000000, 1.000000],
    [0.052336, 0.034899, 0.017452, 0.999848, 0.999391, 0.998630],
    [0.104528, 0.069756, 0.034899, 0.999391, 0.997564, 0.994522],
    [0.156434, 0.104528, 0.052336, 0.998630, 0.994522, 0.987688],
    [0.207912, 0.139173, 0.069756, 0.997564, 0.990268, 0.978148],
    [0.258819, 0.173648, 0.087156, 0.996195, 0.984808, 0.965926],
    [0.309017, 0.207912, 0.104528, 0.994522, 0.978148, 0.951057],
    [0.358368, 0.241922, 0.121869, 0.992546, 0.970296, 0.933580],
    [0.406737, 0.275637, 0.139173, 0.990268, 0.961262, 0.913545],
    [0.453990, 0.309017, 0.156434, 0.987688, 0.951057, 0.891007],
    [0.500000, 0.342020, 0.173648, 0.984808, 0.939693, 0.866025],
    [0.544639, 0.374607, 0.190809, 0.981627, 0.927184, 0.838671],
    [0.587785, 0.406737, 0.207912, 0.978148, 0.913545, 0.809017],
    [0.629320, 0.438371, 0.224951, 0.974370, 0.898794, 0.777146],
    [0.669131, 0.469472, 0.241922, 0.970296, 0.882948, 0.743145],
    [0.707107, 0.500000, 0.258819, 0.965926, 0.866025, 0.707107],
    [0.743145, 0.529919, 0.275637, 0.961262, 0.848048, 0.669131],
    [0.777146, 0.559193, 0.292372, 0.956305, 0.829038, 0.629320],
    [0.809017, 0.587785, 0.309017, 0.951057, 0.809017, 0.587785],
    [0.838671, 0.615661, 0.325568, 0.945519, 0.788011, 0.544639],
    [0.866025, 0.642788, 0.342020, 0.939693, 0.766044, 0.500000],
    [0.891007, 0.669131, 0.358368, 0.933580, 0.743145, 0.453990],
    [0.913545, 0.694658, 0.374607, 0.927184, 0.719340, 0.406737],
    [0.933580, 0.719340, 0.390731, 0.920505, 0.694658, 0.358368],
    [0.951057, 0.743145, 0.406737, 0.913545, 0.669131, 0.309017],
    [0.965926, 0.766044, 0.422618, 0.906308, 0.642788, 0.258819],
    [0.978148, 0.788011, 0.438371, 0.898794, 0.615661, 0.207912],
    [0.987688, 0.809017, 0.453990, 0.891007, 0.587785, 0.156434],
    [0.994522, 0.829038, 0.469472, 0.882948, 0.559193, 0.104528],
    [0.998630, 0.848048, 0.484810, 0.874620, 0.529919, 0.052336],
    [1.000000, 0.866025, 0.500000, 0.866025, 0.500000, 0.000000],
    [0.998630, 0.882948, 0.515038, 0.857167, 0.469472, -0.052336],
    [0.994522, 0.898794, 0.529919, 0.848048, 0.438371, -0.104528],
    [0.987688, 0.913545, 0.544639, 0.838671, 0.406737, -0.156434],
    [0.978148, 0.927184, 0.559193, 0.829038, 0.374607, -0.207912],
    [0.965926, 0.939693, 0.573576, 0.819152, 0.342020, -0.258819],
    [0.951057, 0.951057, 0.587785, 0.809017, 0.309017, -0.309017],
    [0.933580, 0.961262, 0.601815, 0.798636, 0.275637, -0.358368],
    [0.913545, 0.970296, 0.615661, 0.788011, 0.241922, -0.406737],
    [0.891007, 0.978148, 0.629320, 0.777146, 0.207912, -0.453990],
    [0.866025, 0.984808, 0.642788, 0.766044, 0.173648, -0.500000],
    [0.838671, 0.990268, 0.656059, 0.754710, 0.139173, -0.544639],
    [0.809017, 0.994522, 0.669131, 0.743145, 0.104528, -0.587785],
    [0.777146, 0.997564, 0.681998, 0.731354, 0.069756, -0.629320],
    [0.743145, 0.999391, 0.694658, 0.719340, 0.034899, -0.669131],
    [0.707107, 1.000000, 0.707107, 0.707107, 0.000000, -0.707107],
    [0.669131, 0.999391, 0.719340, 0.694658, -0.034899, -0.743145],
    [0.629320, 0.997564, 0.731354, 0.681998, -0.069756, -0.777146],
    [0.587785, 0.994522, 0.743145, 0.669131, -0.104528, -0.809017],
    [0.544639, 0.990268, 0.754710, 0.656059, -0.139173, -0.838671],
    [0.500000, 0.984808, 0.766044, 0.642788, -0.173648, -0.866025],
    [0.453990, 0.978148, 0.777146, 0.629320, -0.207912, -0.891007],
    [0.406737, 0.970296, 0.788011, 0.615661, -0.241922, -0.913545],
    [0.358368, 0.961262, 0.798636, 0.601815, -0.275637, -0.933580],
    [0.309017, 0.951057, 0.809017, 0.587785, -0.309017, -0.951057],
    [0.258819, 0.939693, 0.819152, 0.573576, -0.342020, -0.965926],
    [0.207912, 0.927184, 0.829038, 0.559193, -0.374607, -0.978148],
    [0.156434, 0.913545, 0.838671, 0.544639, -0.406737, -0.987688],
    [0.104528, 0.898794, 0.848048, 0.529919, -0.438371, -0.994522],
    [0.052336, 0.882948, 0.857167, 0.515038, -0.469472, -0.998630],
    [0.000000, 0.866025, 0.866025, 0.500000, -0.500000, -1.000000],
    [-0.052336, 0.848048, 0.874620, 0.484810, -0.529919, -0.998630],
    [-0.104528, 0.829038, 0.882948, 0.469472, -0.559193, -0.994522],
    [-0.156434, 0.809017, 0.891007, 0.453990, -0.587785, -0.987688],
    [-0.207912, 0.788011, 0.898794, 0.438371, -0.615661, -0.978148],
    [-0.258819, 0.766044, 0.906308, 0.422618, -0.642788, -0.965926],
    [-0.309017, 0.743145, 0.913545, 0.406737, -0.669131, -0.951057],
    [-0.358368, 0.719340, 0.920505, 0.390731, -0.694658, -0.933580],
    [-0.406737, 0.694658, 0.927184, 0.374607, -0.719340, -0.913545],
    [-0.453990, 0.669131, 0.933580, 0.358368, -0.743145, -0.891007],
    [-0.500000, 0.642788, 0.939693, 0.342020, -0.766044, -0.866025],
    [-0.544639, 0.615661, 0.945519, 0.325568, -0.788011, -0.838671],
    [-0.587785, 0.587785, 0.951057, 0.309017, -0.809017, -0.809017],
    [-0.629320, 0.559193, 0.956305, 0.292372, -0.829038, -0.777146],
    [-0.669131, 0.529919, 0.961262, 0.275637, -0.848048, -0.743145],
    [-0.707107, 0.500000, 0.965926, 0.258819, -0.866025, -0.707107],
    [-0.743145, 0.469472, 0.970296, 0.241922, -0.882948, -0.669131],
    [-0.777146, 0.438371, 0.974370, 0.224951, -0.898794, -0.629320],
    [-0.809017, 0.406737, 0.978148, 0.207912, -0.913545, -0.587785],
    [-0.838671, 0.374607, 0.981627, 0.190809, -0.927184, -0.544639],
    [-0.866025, 0.342020, 0.984808, 0.173648, -0.939693, -0.500000],
    [-0.891007, 0.309017, 0.987688, 0.156434, -0.951057, -0.453990],
    [-0.913545, 0.275637, 0.990268, 0.139173, -0.961262, -0.406737],
    [-0.933580, 0.241922, 0.992546, 0.121869, -0.970296, -0.358368],
    [-0.951057, 0.207912, 0.994522, 0.104528, -0.978148, -0.309017],
    [-0.965926, 0.173648, 0.996195, 0.087156, -0.984808, -0.258819],
    [-0.978148, 0.139173, 0.997564, 0.069756, -0.990268, -0.207912],
    [-0.987688, 0.104528, 0.998630, 0.052336, -0.994522, -0.156434],
    [-0.994522, 0.069756, 0.999391, 0.034899, -0.997564, -0.104528],
    [-0.998630, 0.034899, 0.999848, 0.017452, -0.999391, -0.052336],
    [-1.000000, 0.000000, 1.000000, 0.000000, -1.000000, -0.000000],
    [-0.998630, -0.034899, 0.999848, -0.017452, -0.999391, 0.052336],
    [-0.994522, -0.069756, 0.999391, -0.034899, -0.997564, 0.104528],
    [-0.987688, -0.104528, 0.998630, -0.052336, -0.994522, 0.156434],
    [-0.978148, -0.139173, 0.997564, -0.069756, -0.990268, 0.207912],
    [-0.965926, -0.173648, 0.996195, -0.087156, -0.984808, 0.258819],
    [-0.951057, -0.207912, 0.994522, -0.104528, -0.978148, 0.309017],
    [-0.933580, -0.241922, 0.992546, -0.121869, -0.970296, 0.358368],
    [-0.913545, -0.275637, 0.990268, -0.139173, -0.961262, 0.406737],
    [-0.891007, -0.309017, 0.987688, -0.156434, -0.951057, 0.453990],
    [-0.866025, -0.342020, 0.984808, -0.173648, -0.939693, 0.500000],
    [-0.838671, -0.374607, 0.981627, -0.190809, -0.927184, 0.544639],
    [-0.809017, -0.406737, 0.978148, -0.207912, -0.913545, 0.587785],
    [-0.777146, -0.438371, 0.974370, -0.224951, -0.898794, 0.629320],
    [-0.743145, -0.469472, 0.970296, -0.241922, -0.882948, 0.669131],
    [-0.707107, -0.500000, 0.965926, -0.258819, -0.866025, 0.707107],
    [-0.669131, -0.529919, 0.961262, -0.275637, -0.848048, 0.743145],
    [-0.629320, -0.559193, 0.956305, -0.292372, -0.829038, 0.777146],
    [-0.587785, -0.587785, 0.951057, -0.309017, -0.809017, 0.809017],
    [-0.544639, -0.615661, 0.945519, -0.325568, -0.788011, 0.838671],
    [-0.500000, -0.642788, 0.939693, -0.342020, -0.766044, 0.866025],
    [-0.453990, -0.669131, 0.933580, -0.358368, -0.743145, 0.891007],
    [-0.406737, -0.694658, 0.927184, -0.374607, -0.719340, 0.913545],
    [-0.358368, -0.719340, 0.920505, -0.390731, -0.694658, 0.933580],
    [-0.309017, -0.743145, 0.913545, -0.406737, -0.669131, 0.951057],
    [-0.258819, -0.766044, 0.906308, -0.422618, -0.642788, 0.965926],
    [-0.207912, -0.788011, 0.898794, -0.438371, -0.615661, 0.978148],
    [-0.156434, -0.809017, 0.891007, -0.453990, -0.587785, 0.987688],
    [-0.104528, -0.829038, 0.882948, -0.469472, -0.559193, 0.994522],
    [-0.052336, -0.848048, 0.874620, -0.484810, -0.529919, 0.998630],
    [-0.000000, -0.866025, 0.866025, -0.500000, -0.500000, 1.000000],
    [0.052336, -0.882948, 0.857167, -0.515038, -0.469472, 0.998630],
    [0.104528, -0.898794, 0.848048, -0.529919, -0.438371, 0.994522],
    [0.156434, -0.913545, 0.838671, -0.544639, -0.406737, 0.987688],
    [0.207912, -0.927184, 0.829038, -0.559193, -0.374607, 0.978148],
    [0.258819, -0.939693, 0.819152, -0.573576, -0.342020, 0.965926],
    [0.309017, -0.951057, 0.809017, -0.587785, -0.309017, 0.951057],
    [0.358368, -0.961262, 0.798636, -0.601815, -0.275637, 0.933580],
    [0.406737, -0.970296, 0.788011, -0.615661, -0.241922, 0.913545],
    [0.453990, -0.978148, 0.777146, -0.629320, -0.207912, 0.891007],
    [0.500000, -0.984808, 0.766044, -0.642788, -0.173648, 0.866025],
    [0.544639, -0.990268, 0.754710, -0.656059, -0.139173, 0.838671],
    [0.587785, -0.994522, 0.743145, -0.669131, -0.104528, 0.809017],
    [0.629320, -0.997564, 0.731354, -0.681998, -0.069756, 0.777146],
    [0.669131, -0.999391, 0.719340, -0.694658, -0.034899, 0.743145],
    [0.707107, -1.000000, 0.707107, -0.707107, -0.000000, 0.707107],
    [0.743145, -0.999391, 0.694658, -0.719340, 0.034899, 0.669131],
    [0.777146, -0.997564, 0.681998, -0.731354, 0.069756, 0.629320],
    [0.809017, -0.994522, 0.669131, -0.743145, 0.104528, 0.587785],
    [0.838671, -0.990268, 0.656059, -0.754710, 0.139173, 0.544639],
    [0.866025, -0.984808, 0.642788, -0.766044, 0.173648, 0.500000],
    [0.891007, -0.978148, 0.629320, -0.777146, 0.207912, 0.453990],
    [0.913545, -0.970296, 0.615661, -0.788011, 0.241922, 0.406737],
    [0.933580, -0.961262, 0.601815, -0.798636, 0.275637, 0.358368],
    [0.951057, -0.951057, 0.587785, -0.809017, 0.309017, 0.309017],
    [0.965926, -0.939693, 0.573576, -0.819152, 0.342020, 0.258819],
    [0.978148, -0.927184, 0.559193, -0.829038, 0.374607, 0.207912],
    [0.987688, -0.913545, 0.544639, -0.838671, 0.406737, 0.156434],
    [0.994522, -0.898794, 0.529919, -0.848048, 0.438371, 0.104528],
    [0.998630, -0.882948, 0.515038, -0.857167, 0.469472, 0.052336],
    [1.000000, -0.866025, 0.500000, -0.866025, 0.500000, 0.000000],
    [0.998630, -0.848048, 0.484810, -0.874620, 0.529919, -0.052336],
    [0.994522, -0.829038, 0.469472, -0.882948, 0.559193, -0.104528],
    [0.987688, -0.809017, 0.453990, -0.891007, 0.587785, -0.156434],
    [0.978148, -0.788011, 0.438371, -0.898794, 0.615661, -0.207912],
    [0.965926, -0.766044, 0.422618, -0.906308, 0.642788, -0.258819],
    [0.951057, -0.743145, 0.406737, -0.913545, 0.669131, -0.309017],
    [0.933580, -0.719340, 0.390731, -0.920505, 0.694658, -0.358368],
    [0.913545, -0.694658, 0.374607, -0.927184, 0.719340, -0.406737],
    [0.891007, -0.669131, 0.358368, -0.933580, 0.743145, -0.453990],
    [0.866025, -0.642788, 0.342020, -0.939693, 0.766044, -0.500000],
    [0.838671, -0.615661, 0.325568, -0.945519, 0.788011, -0.544639],
    [0.809017, -0.587785, 0.309017, -0.951057, 0.809017, -0.587785],
    [0.777146, -0.559193, 0.292372, -0.956305, 0.829038, -0.629320],
    [0.743145, -0.529919, 0.275637, -0.961262, 0.848048, -0.669131],
    [0.707107, -0.500000, 0.258819, -0.965926, 0.866025, -0.707107],
    [0.669131, -0.469472, 0.241922, -0.970296, 0.882948, -0.743145],
    [0.629320, -0.438371, 0.224951, -0.974370, 0.898794, -0.777146],
    [0.587785, -0.406737, 0.207912, -0.978148, 0.913545, -0.809017],
    [0.544639, -0.374607, 0.190809, -0.981627, 0.927184, -0.838671],
    [0.500000, -0.342020, 0.173648, -0.984808, 0.939693, -0.866025],
    [0.453990, -0.309017, 0.156434, -0.987688, 0.951057, -0.891007],
    [0.406737, -0.275637, 0.139173, -0.990268, 0.961262, -0.913545],
    [0.358368, -0.241922, 0.121869, -0.992546, 0.970296, -0.933580],
    [0.309017, -0.207912, 0.104528, -0.994522, 0.978148, -0.951057],
    [0.258819, -0.173648, 0.087156, -0.996195, 0.984808, -0.965926],
    [0.207912, -0.139173, 0.069756, -0.997564, 0.990268, -0.978148],
    [0.156434, -0.104528, 0.052336, -0.998630, 0.994522, -0.987688],
    [0.104528, -0.069756, 0.034899, -0.999391, 0.997564, -0.994522],
    [0.052336, -0.034899, 0.017452, -0.999848, 0.999391, -0.998630],
    [0.000000, -0.000000, 0.000000, -1.000000, 1.000000, -1.000000],
    [-0.052336, 0.034899, -0.017452, -0.999848, 0.999391, -0.998630],
    [-0.104528, 0.069756, -0.034899, -0.999391, 0.997564, -0.994522],
    [-0.156434, 0.104528, -0.052336, -0.998630, 0.994522, -0.987688],
    [-0.207912, 0.139173, -0.069756, -0.997564, 0.990268, -0.978148],
    [-0.258819, 0.173648, -0.087156, -0.996195, 0.984808, -0.965926],
    [-0.309017, 0.207912, -0.104528, -0.994522, 0.978148, -0.951057],
    [-0.358368, 0.241922, -0.121869, -0.992546, 0.970296, -0.933580],
    [-0.406737, 0.275637, -0.139173, -0.990268, 0.961262, -0.913545],
    [-0.453990, 0.309017, -0.156434, -0.987688, 0.951057, -0.891007],
    [-0.500000, 0.342020, -0.173648, -0.984808, 0.939693, -0.866025],
    [-0.544639, 0.374607, -0.190809, -0.981627, 0.927184, -0.838671],
    [-0.587785, 0.406737, -0.207912, -0.978148, 0.913545, -0.809017],
    [-0.629320, 0.438371, -0.224951, -0.974370, 0.898794, -0.777146],
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    [0.933580, 0.358368, 0.807359, 0.579484, 0.111222,
     0.633837, 0.736898, 0.232180, 0.036385],
    [0.939693, 0.342020, 0.824533, 0.556670, 0.101306,
     0.664885, 0.715274, 0.212865, 0.031630],
    [0.945519, 0.325568, 0.841008, 0.533178, 0.091794,
     0.694969, 0.691816, 0.194075, 0.027281],
    [0.951057, 0.309017, 0.856763, 0.509037, 0.082698,
     0.724012, 0.666583, 0.175868, 0.023329],
    [0.956305, 0.292372, 0.871778, 0.484275, 0.074029,
     0.751940, 0.639639, 0.158301, 0.019758],
    [0.961262, 0.275637, 0.886036, 0.458924, 0.065797,
     0.778680, 0.611050, 0.141427, 0.016556],
    [0.965926, 0.258819, 0.899519, 0.433013, 0.058013,
     0.804164, 0.580889, 0.125300, 0.013707],
    [0.970296, 0.241922, 0.912211, 0.406574, 0.050685,
     0.828326, 0.549233, 0.109969, 0.011193],
    [0.974370, 0.224951, 0.924096, 0.379641, 0.043823,
     0.851105, 0.516162, 0.095481, 0.008999],
    [0.978148, 0.207912, 0.935159, 0.352244, 0.037436,
     0.872441, 0.481759, 0.081880, 0.007105],
    [0.981627, 0.190809, 0.945388, 0.324419, 0.031530,
     0.892279, 0.446114, 0.069209, 0.005492],
    [0.984808, 0.173648, 0.954769, 0.296198, 0.026114,
     0.910569, 0.409317, 0.057505, 0.004140],
    [0.987688, 0.156434, 0.963292, 0.267617, 0.021193,
     0.927262, 0.371463, 0.046806, 0.003026],
    [0.990268, 0.139173, 0.970946, 0.238709, 0.016774,
     0.942316, 0.332649, 0.037143, 0.002131],
    [0.992546, 0.121869, 0.977722, 0.209511, 0.012862,
     0.955693, 0.292976, 0.028547, 0.001431],
    [0.994522, 0.104528, 0.983611, 0.180057, 0.009462,
     0.967356, 0.252544, 0.021043, 0.000903],
    [0.996195, 0.087156, 0.988606, 0.150384, 0.006578,
     0.977277, 0.211460, 0.014654, 0.000523],
    [0.997564, 0.069756, 0.992701, 0.120527, 0.004214,
     0.985429, 0.169828, 0.009400, 0.000268],
    [0.998630, 0.052336, 0.995891, 0.090524, 0.002372,
     0.991791, 0.127757, 0.005297, 0.000113],
    [0.999391, 0.034899, 0.998173, 0.060411, 0.001055,
     0.996348, 0.085356, 0.002357, 0.000034],
    [0.999848, 0.017452, 0.999543, 0.030224, 0.000264,
     0.999086, 0.042733, 0.000590, 0.000004],
    [1.000000, -0.000000, 1.000000, -0.000000, 0.000000,
     1.000000, -0.000000, 0.000000, -0.000000],
  ],
];


/** @type {Number} */
exports.SPHERICAL_HARMONICS_AZIMUTH_RESOLUTION =
  exports.SPHERICAL_HARMONICS[0].length;


/** @type {Number} */
exports.SPHERICAL_HARMONICS_ELEVATION_RESOLUTION =
  exports.SPHERICAL_HARMONICS[1].length;


/**
 * The maximum allowed ambisonic order.
 * @type {Number}
 */
exports.SPHERICAL_HARMONICS_MAX_ORDER =
  exports.SPHERICAL_HARMONICS[0][0].length / 2;


/**
 * Pre-computed per-band weighting coefficients for producing energy-preserving
 * Max-Re sources.
 */
exports.MAX_RE_WEIGHTS =
[
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.000000, 1.000000, 1.000000, 1.000000],
  [1.003236, 1.002156, 0.999152, 0.990038],
  [1.032370, 1.021194, 0.990433, 0.898572],
  [1.062694, 1.040231, 0.979161, 0.799806],
  [1.093999, 1.058954, 0.964976, 0.693603],
  [1.126003, 1.077006, 0.947526, 0.579890],
  [1.158345, 1.093982, 0.926474, 0.458690],
  [1.190590, 1.109437, 0.901512, 0.330158],
  [1.222228, 1.122890, 0.872370, 0.194621],
  [1.252684, 1.133837, 0.838839, 0.052614],
  [1.281987, 1.142358, 0.801199, 0.000000],
  [1.312073, 1.150207, 0.760839, 0.000000],
  [1.343011, 1.157424, 0.717799, 0.000000],
  [1.374649, 1.163859, 0.671999, 0.000000],
  [1.406809, 1.169354, 0.623371, 0.000000],
  [1.439286, 1.173739, 0.571868, 0.000000],
  [1.471846, 1.176837, 0.517465, 0.000000],
  [1.504226, 1.178465, 0.460174, 0.000000],
  [1.536133, 1.178438, 0.400043, 0.000000],
  [1.567253, 1.176573, 0.337165, 0.000000],
  [1.597247, 1.172695, 0.271688, 0.000000],
  [1.625766, 1.166645, 0.203815, 0.000000],
  [1.652455, 1.158285, 0.133806, 0.000000],
  [1.676966, 1.147506, 0.061983, 0.000000],
  [1.699006, 1.134261, 0.000000, 0.000000],
  [1.720224, 1.119789, 0.000000, 0.000000],
  [1.741631, 1.104810, 0.000000, 0.000000],
  [1.763183, 1.089330, 0.000000, 0.000000],
  [1.784837, 1.073356, 0.000000, 0.000000],
  [1.806548, 1.056898, 0.000000, 0.000000],
  [1.828269, 1.039968, 0.000000, 0.000000],
  [1.849952, 1.022580, 0.000000, 0.000000],
  [1.871552, 1.004752, 0.000000, 0.000000],
  [1.893018, 0.986504, 0.000000, 0.000000],
  [1.914305, 0.967857, 0.000000, 0.000000],
  [1.935366, 0.948837, 0.000000, 0.000000],
  [1.956154, 0.929471, 0.000000, 0.000000],
  [1.976625, 0.909790, 0.000000, 0.000000],
  [1.996736, 0.889823, 0.000000, 0.000000],
  [2.016448, 0.869607, 0.000000, 0.000000],
  [2.035721, 0.849175, 0.000000, 0.000000],
  [2.054522, 0.828565, 0.000000, 0.000000],
  [2.072818, 0.807816, 0.000000, 0.000000],
  [2.090581, 0.786964, 0.000000, 0.000000],
  [2.107785, 0.766051, 0.000000, 0.000000],
  [2.124411, 0.745115, 0.000000, 0.000000],
  [2.140439, 0.724196, 0.000000, 0.000000],
  [2.155856, 0.703332, 0.000000, 0.000000],
  [2.170653, 0.682561, 0.000000, 0.000000],
  [2.184823, 0.661921, 0.000000, 0.000000],
  [2.198364, 0.641445, 0.000000, 0.000000],
  [2.211275, 0.621169, 0.000000, 0.000000],
  [2.223562, 0.601125, 0.000000, 0.000000],
  [2.235230, 0.581341, 0.000000, 0.000000],
  [2.246289, 0.561847, 0.000000, 0.000000],
  [2.256751, 0.542667, 0.000000, 0.000000],
  [2.266631, 0.523826, 0.000000, 0.000000],
  [2.275943, 0.505344, 0.000000, 0.000000],
  [2.284707, 0.487239, 0.000000, 0.000000],
  [2.292939, 0.469528, 0.000000, 0.000000],
  [2.300661, 0.452225, 0.000000, 0.000000],
  [2.307892, 0.435342, 0.000000, 0.000000],
  [2.314654, 0.418888, 0.000000, 0.000000],
  [2.320969, 0.402870, 0.000000, 0.000000],
  [2.326858, 0.387294, 0.000000, 0.000000],
  [2.332343, 0.372164, 0.000000, 0.000000],
  [2.337445, 0.357481, 0.000000, 0.000000],
  [2.342186, 0.343246, 0.000000, 0.000000],
  [2.346585, 0.329458, 0.000000, 0.000000],
  [2.350664, 0.316113, 0.000000, 0.000000],
  [2.354442, 0.303208, 0.000000, 0.000000],
  [2.357937, 0.290738, 0.000000, 0.000000],
  [2.361168, 0.278698, 0.000000, 0.000000],
  [2.364152, 0.267080, 0.000000, 0.000000],
  [2.366906, 0.255878, 0.000000, 0.000000],
  [2.369446, 0.245082, 0.000000, 0.000000],
  [2.371786, 0.234685, 0.000000, 0.000000],
  [2.373940, 0.224677, 0.000000, 0.000000],
  [2.375923, 0.215048, 0.000000, 0.000000],
  [2.377745, 0.205790, 0.000000, 0.000000],
  [2.379421, 0.196891, 0.000000, 0.000000],
  [2.380959, 0.188342, 0.000000, 0.000000],
  [2.382372, 0.180132, 0.000000, 0.000000],
  [2.383667, 0.172251, 0.000000, 0.000000],
  [2.384856, 0.164689, 0.000000, 0.000000],
  [2.385945, 0.157435, 0.000000, 0.000000],
  [2.386943, 0.150479, 0.000000, 0.000000],
  [2.387857, 0.143811, 0.000000, 0.000000],
  [2.388694, 0.137421, 0.000000, 0.000000],
  [2.389460, 0.131299, 0.000000, 0.000000],
  [2.390160, 0.125435, 0.000000, 0.000000],
  [2.390801, 0.119820, 0.000000, 0.000000],
  [2.391386, 0.114445, 0.000000, 0.000000],
  [2.391921, 0.109300, 0.000000, 0.000000],
  [2.392410, 0.104376, 0.000000, 0.000000],
  [2.392857, 0.099666, 0.000000, 0.000000],
  [2.393265, 0.095160, 0.000000, 0.000000],
  [2.393637, 0.090851, 0.000000, 0.000000],
  [2.393977, 0.086731, 0.000000, 0.000000],
  [2.394288, 0.082791, 0.000000, 0.000000],
  [2.394571, 0.079025, 0.000000, 0.000000],
  [2.394829, 0.075426, 0.000000, 0.000000],
  [2.395064, 0.071986, 0.000000, 0.000000],
  [2.395279, 0.068699, 0.000000, 0.000000],
  [2.395475, 0.065558, 0.000000, 0.000000],
  [2.395653, 0.062558, 0.000000, 0.000000],
  [2.395816, 0.059693, 0.000000, 0.000000],
  [2.395964, 0.056955, 0.000000, 0.000000],
  [2.396099, 0.054341, 0.000000, 0.000000],
  [2.396222, 0.051845, 0.000000, 0.000000],
  [2.396334, 0.049462, 0.000000, 0.000000],
  [2.396436, 0.047186, 0.000000, 0.000000],
  [2.396529, 0.045013, 0.000000, 0.000000],
  [2.396613, 0.042939, 0.000000, 0.000000],
  [2.396691, 0.040959, 0.000000, 0.000000],
  [2.396761, 0.039069, 0.000000, 0.000000],
  [2.396825, 0.037266, 0.000000, 0.000000],
  [2.396883, 0.035544, 0.000000, 0.000000],
  [2.396936, 0.033901, 0.000000, 0.000000],
  [2.396984, 0.032334, 0.000000, 0.000000],
  [2.397028, 0.030838, 0.000000, 0.000000],
  [2.397068, 0.029410, 0.000000, 0.000000],
  [2.397104, 0.028048, 0.000000, 0.000000],
  [2.397137, 0.026749, 0.000000, 0.000000],
  [2.397167, 0.025509, 0.000000, 0.000000],
  [2.397194, 0.024326, 0.000000, 0.000000],
  [2.397219, 0.023198, 0.000000, 0.000000],
  [2.397242, 0.022122, 0.000000, 0.000000],
  [2.397262, 0.021095, 0.000000, 0.000000],
  [2.397281, 0.020116, 0.000000, 0.000000],
  [2.397298, 0.019181, 0.000000, 0.000000],
  [2.397314, 0.018290, 0.000000, 0.000000],
  [2.397328, 0.017441, 0.000000, 0.000000],
  [2.397341, 0.016630, 0.000000, 0.000000],
  [2.397352, 0.015857, 0.000000, 0.000000],
  [2.397363, 0.015119, 0.000000, 0.000000],
  [2.397372, 0.014416, 0.000000, 0.000000],
  [2.397381, 0.013745, 0.000000, 0.000000],
  [2.397389, 0.013106, 0.000000, 0.000000],
  [2.397396, 0.012496, 0.000000, 0.000000],
  [2.397403, 0.011914, 0.000000, 0.000000],
  [2.397409, 0.011360, 0.000000, 0.000000],
  [2.397414, 0.010831, 0.000000, 0.000000],
  [2.397419, 0.010326, 0.000000, 0.000000],
  [2.397424, 0.009845, 0.000000, 0.000000],
  [2.397428, 0.009387, 0.000000, 0.000000],
  [2.397432, 0.008949, 0.000000, 0.000000],
  [2.397435, 0.008532, 0.000000, 0.000000],
  [2.397438, 0.008135, 0.000000, 0.000000],
  [2.397441, 0.007755, 0.000000, 0.000000],
  [2.397443, 0.007394, 0.000000, 0.000000],
  [2.397446, 0.007049, 0.000000, 0.000000],
  [2.397448, 0.006721, 0.000000, 0.000000],
  [2.397450, 0.006407, 0.000000, 0.000000],
  [2.397451, 0.006108, 0.000000, 0.000000],
  [2.397453, 0.005824, 0.000000, 0.000000],
  [2.397454, 0.005552, 0.000000, 0.000000],
  [2.397456, 0.005293, 0.000000, 0.000000],
  [2.397457, 0.005046, 0.000000, 0.000000],
  [2.397458, 0.004811, 0.000000, 0.000000],
  [2.397459, 0.004586, 0.000000, 0.000000],
  [2.397460, 0.004372, 0.000000, 0.000000],
  [2.397461, 0.004168, 0.000000, 0.000000],
  [2.397461, 0.003974, 0.000000, 0.000000],
  [2.397462, 0.003788, 0.000000, 0.000000],
  [2.397463, 0.003611, 0.000000, 0.000000],
  [2.397463, 0.003443, 0.000000, 0.000000],
  [2.397464, 0.003282, 0.000000, 0.000000],
  [2.397464, 0.003129, 0.000000, 0.000000],
  [2.397465, 0.002983, 0.000000, 0.000000],
  [2.397465, 0.002844, 0.000000, 0.000000],
  [2.397465, 0.002711, 0.000000, 0.000000],
  [2.397466, 0.002584, 0.000000, 0.000000],
  [2.397466, 0.002464, 0.000000, 0.000000],
  [2.397466, 0.002349, 0.000000, 0.000000],
  [2.397466, 0.002239, 0.000000, 0.000000],
  [2.397467, 0.002135, 0.000000, 0.000000],
  [2.397467, 0.002035, 0.000000, 0.000000],
  [2.397467, 0.001940, 0.000000, 0.000000],
  [2.397467, 0.001849, 0.000000, 0.000000],
  [2.397467, 0.001763, 0.000000, 0.000000],
  [2.397467, 0.001681, 0.000000, 0.000000],
  [2.397468, 0.001602, 0.000000, 0.000000],
  [2.397468, 0.001527, 0.000000, 0.000000],
  [2.397468, 0.001456, 0.000000, 0.000000],
  [2.397468, 0.001388, 0.000000, 0.000000],
  [2.397468, 0.001323, 0.000000, 0.000000],
  [2.397468, 0.001261, 0.000000, 0.000000],
  [2.397468, 0.001202, 0.000000, 0.000000],
  [2.397468, 0.001146, 0.000000, 0.000000],
  [2.397468, 0.001093, 0.000000, 0.000000],
  [2.397468, 0.001042, 0.000000, 0.000000],
  [2.397468, 0.000993, 0.000000, 0.000000],
  [2.397468, 0.000947, 0.000000, 0.000000],
  [2.397468, 0.000902, 0.000000, 0.000000],
  [2.397468, 0.000860, 0.000000, 0.000000],
  [2.397468, 0.000820, 0.000000, 0.000000],
  [2.397469, 0.000782, 0.000000, 0.000000],
  [2.397469, 0.000745, 0.000000, 0.000000],
  [2.397469, 0.000710, 0.000000, 0.000000],
  [2.397469, 0.000677, 0.000000, 0.000000],
  [2.397469, 0.000646, 0.000000, 0.000000],
  [2.397469, 0.000616, 0.000000, 0.000000],
  [2.397469, 0.000587, 0.000000, 0.000000],
  [2.397469, 0.000559, 0.000000, 0.000000],
  [2.397469, 0.000533, 0.000000, 0.000000],
  [2.397469, 0.000508, 0.000000, 0.000000],
  [2.397469, 0.000485, 0.000000, 0.000000],
  [2.397469, 0.000462, 0.000000, 0.000000],
  [2.397469, 0.000440, 0.000000, 0.000000],
  [2.397469, 0.000420, 0.000000, 0.000000],
  [2.397469, 0.000400, 0.000000, 0.000000],
  [2.397469, 0.000381, 0.000000, 0.000000],
  [2.397469, 0.000364, 0.000000, 0.000000],
  [2.397469, 0.000347, 0.000000, 0.000000],
  [2.397469, 0.000330, 0.000000, 0.000000],
  [2.397469, 0.000315, 0.000000, 0.000000],
  [2.397469, 0.000300, 0.000000, 0.000000],
  [2.397469, 0.000286, 0.000000, 0.000000],
  [2.397469, 0.000273, 0.000000, 0.000000],
  [2.397469, 0.000260, 0.000000, 0.000000],
  [2.397469, 0.000248, 0.000000, 0.000000],
  [2.397469, 0.000236, 0.000000, 0.000000],
  [2.397469, 0.000225, 0.000000, 0.000000],
  [2.397469, 0.000215, 0.000000, 0.000000],
  [2.397469, 0.000205, 0.000000, 0.000000],
  [2.397469, 0.000195, 0.000000, 0.000000],
  [2.397469, 0.000186, 0.000000, 0.000000],
  [2.397469, 0.000177, 0.000000, 0.000000],
  [2.397469, 0.000169, 0.000000, 0.000000],
  [2.397469, 0.000161, 0.000000, 0.000000],
  [2.397469, 0.000154, 0.000000, 0.000000],
  [2.397469, 0.000147, 0.000000, 0.000000],
  [2.397469, 0.000140, 0.000000, 0.000000],
  [2.397469, 0.000133, 0.000000, 0.000000],
  [2.397469, 0.000127, 0.000000, 0.000000],
  [2.397469, 0.000121, 0.000000, 0.000000],
  [2.397469, 0.000115, 0.000000, 0.000000],
  [2.397469, 0.000110, 0.000000, 0.000000],
  [2.397469, 0.000105, 0.000000, 0.000000],
  [2.397469, 0.000100, 0.000000, 0.000000],
  [2.397469, 0.000095, 0.000000, 0.000000],
  [2.397469, 0.000091, 0.000000, 0.000000],
  [2.397469, 0.000087, 0.000000, 0.000000],
  [2.397469, 0.000083, 0.000000, 0.000000],
  [2.397469, 0.000079, 0.000000, 0.000000],
  [2.397469, 0.000075, 0.000000, 0.000000],
  [2.397469, 0.000071, 0.000000, 0.000000],
  [2.397469, 0.000068, 0.000000, 0.000000],
  [2.397469, 0.000065, 0.000000, 0.000000],
  [2.397469, 0.000062, 0.000000, 0.000000],
  [2.397469, 0.000059, 0.000000, 0.000000],
  [2.397469, 0.000056, 0.000000, 0.000000],
  [2.397469, 0.000054, 0.000000, 0.000000],
  [2.397469, 0.000051, 0.000000, 0.000000],
  [2.397469, 0.000049, 0.000000, 0.000000],
  [2.397469, 0.000046, 0.000000, 0.000000],
  [2.397469, 0.000044, 0.000000, 0.000000],
  [2.397469, 0.000042, 0.000000, 0.000000],
  [2.397469, 0.000040, 0.000000, 0.000000],
  [2.397469, 0.000038, 0.000000, 0.000000],
  [2.397469, 0.000037, 0.000000, 0.000000],
  [2.397469, 0.000035, 0.000000, 0.000000],
  [2.397469, 0.000033, 0.000000, 0.000000],
  [2.397469, 0.000032, 0.000000, 0.000000],
  [2.397469, 0.000030, 0.000000, 0.000000],
  [2.397469, 0.000029, 0.000000, 0.000000],
  [2.397469, 0.000027, 0.000000, 0.000000],
  [2.397469, 0.000026, 0.000000, 0.000000],
  [2.397469, 0.000025, 0.000000, 0.000000],
  [2.397469, 0.000024, 0.000000, 0.000000],
  [2.397469, 0.000023, 0.000000, 0.000000],
  [2.397469, 0.000022, 0.000000, 0.000000],
  [2.397469, 0.000021, 0.000000, 0.000000],
  [2.397469, 0.000020, 0.000000, 0.000000],
  [2.397469, 0.000019, 0.000000, 0.000000],
  [2.397469, 0.000018, 0.000000, 0.000000],
  [2.397469, 0.000017, 0.000000, 0.000000],
  [2.397469, 0.000016, 0.000000, 0.000000],
  [2.397469, 0.000015, 0.000000, 0.000000],
  [2.397469, 0.000015, 0.000000, 0.000000],
  [2.397469, 0.000014, 0.000000, 0.000000],
  [2.397469, 0.000013, 0.000000, 0.000000],
  [2.397469, 0.000013, 0.000000, 0.000000],
  [2.397469, 0.000012, 0.000000, 0.000000],
  [2.397469, 0.000012, 0.000000, 0.000000],
  [2.397469, 0.000011, 0.000000, 0.000000],
  [2.397469, 0.000011, 0.000000, 0.000000],
  [2.397469, 0.000010, 0.000000, 0.000000],
  [2.397469, 0.000010, 0.000000, 0.000000],
  [2.397469, 0.000009, 0.000000, 0.000000],
  [2.397469, 0.000009, 0.000000, 0.000000],
  [2.397469, 0.000008, 0.000000, 0.000000],
  [2.397469, 0.000008, 0.000000, 0.000000],
  [2.397469, 0.000008, 0.000000, 0.000000],
  [2.397469, 0.000007, 0.000000, 0.000000],
  [2.397469, 0.000007, 0.000000, 0.000000],
  [2.397469, 0.000007, 0.000000, 0.000000],
  [2.397469, 0.000006, 0.000000, 0.000000],
  [2.397469, 0.000006, 0.000000, 0.000000],
  [2.397469, 0.000006, 0.000000, 0.000000],
  [2.397469, 0.000005, 0.000000, 0.000000],
  [2.397469, 0.000005, 0.000000, 0.000000],
  [2.397469, 0.000005, 0.000000, 0.000000],
  [2.397469, 0.000005, 0.000000, 0.000000],
  [2.397469, 0.000004, 0.000000, 0.000000],
  [2.397469, 0.000004, 0.000000, 0.000000],
  [2.397469, 0.000004, 0.000000, 0.000000],
  [2.397469, 0.000004, 0.000000, 0.000000],
  [2.397469, 0.000004, 0.000000, 0.000000],
  [2.397469, 0.000004, 0.000000, 0.000000],
  [2.397469, 0.000003, 0.000000, 0.000000],
  [2.397469, 0.000003, 0.000000, 0.000000],
  [2.397469, 0.000003, 0.000000, 0.000000],
  [2.397469, 0.000003, 0.000000, 0.000000],
  [2.397469, 0.000003, 0.000000, 0.000000],
  [2.397469, 0.000003, 0.000000, 0.000000],
  [2.397469, 0.000003, 0.000000, 0.000000],
  [2.397469, 0.000002, 0.000000, 0.000000],
  [2.397469, 0.000002, 0.000000, 0.000000],
  [2.397469, 0.000002, 0.000000, 0.000000],
  [2.397469, 0.000002, 0.000000, 0.000000],
  [2.397469, 0.000002, 0.000000, 0.000000],
  [2.397469, 0.000002, 0.000000, 0.000000],
  [2.397469, 0.000002, 0.000000, 0.000000],
  [2.397469, 0.000002, 0.000000, 0.000000],
  [2.397469, 0.000002, 0.000000, 0.000000],
  [2.397469, 0.000002, 0.000000, 0.000000],
  [2.397469, 0.000001, 0.000000, 0.000000],
  [2.397469, 0.000001, 0.000000, 0.000000],
  [2.397469, 0.000001, 0.000000, 0.000000],
];


/** @type {Number} */
exports.MAX_RE_WEIGHTS_RESOLUTION = exports.MAX_RE_WEIGHTS.length;
